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A114568
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A vector matrix Markov sequence whose ration approximates the fine structure constant alpha using a single prime 4691 cubic characteristic ploynomial.
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0
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0, 1, 1, 4694, 14074, 22043016, 110093076, 103601931224, 723540388824, 487340138218336, 4368084700020976, 2294361417644038304, 25075040078386453024, 10810705128907312553856, 139223348225447089786176
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| PrimeQ[4691]==True Characteristic polynomial: Expand[(x + 2)*(x - (1 + Sqrt[4691]))*(x - (1 - Sqrt[4691]))] x^3-4694*x-9380 These approximations serve like 22/7 in the approximation of Pi. The cubics also have the benefit of being able to give Weierstrass elliptical functions.
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FORMULA
| M = {{0, 1, 0}, {0, 0, 1}, {9380, 4694, 0}} w[0] = {0, 1, 1} w[n_] := w[n] = M.w[n - 1] a(n) = w[n][[1]]
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MATHEMATICA
| M = {{0, 1, 0}, {0, 0, 1}, {9380, 4694, 0}} w[0] = {0, 1, 1} w[n_] := w[n] = M.w[n - 1] a = Flatten[Table[w[n][[1]], {n, 0, 25}]]
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CROSSREFS
| Sequence in context: A190131 A204073 A114542 * A107544 A092375 A093789
Adjacent sequences: A114565 A114566 A114567 * A114569 A114570 A114571
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KEYWORD
| nonn,uned
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AUTHOR
| Roger Bagula, Feb 16 2006
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